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42
Learning Bayesian belief networks: An approach based on the MDL principle
 Computational Intelligence
, 1994
"... A new approach for learning Bayesian belief networks from raw data is presented. The approach is based on Rissanen's Minimal Description Length (MDL) principle, which is particularly well suited for this task. Our approach does not require any prior assumptions about the distribution being learned. ..."
Abstract

Cited by 188 (8 self)
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A new approach for learning Bayesian belief networks from raw data is presented. The approach is based on Rissanen's Minimal Description Length (MDL) principle, which is particularly well suited for this task. Our approach does not require any prior assumptions about the distribution being learned. In particular, our method can learn unrestricted multiplyconnected belief networks. Furthermore, unlike other approaches our method allows us to tradeo accuracy and complexity in the learned model. This is important since if the learned model is very complex (highly connected) it can be conceptually and computationally intractable. In such a case it would be preferable to use a simpler model even if it is less accurate. The MDL principle o ers a reasoned method for making this tradeo. We also show that our method generalizes previous approaches based on Kullback crossentropy. Experiments have been conducted to demonstrate the feasibility of the approach. Keywords: Knowledge Acquisition � Bayes Nets � Uncertainty Reasoning. 1
A characterization of Markov equivalence classes for acyclic digraphs
, 1995
"... Undirected graphs and acyclic digraphs (ADGs), as well as their mutual extension to chain graphs, are widely used to describe dependencies among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow e ..."
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Cited by 92 (7 self)
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Undirected graphs and acyclic digraphs (ADGs), as well as their mutual extension to chain graphs, are widely used to describe dependencies among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building Bayesian networks for expert systems. Whereas the undirected graph associated with a dependence model is uniquely determined, there may, however, be many ADGs that determine the same dependence ( = Markov) model. Thus, the family of all ADGs with a given set of vertices is naturally partitioned into Markovequivalence classes, each class being associated with a unique statistical model. Statistical procedures, such as model selection or model averaging, that fail to take into account these equivalence classes, may incur substantial computational or other inefficiencies. Here it is shown that each Markovequivalence class is uniquely determined by a single chain graph, the essential graph, that is itself simultaneously Markov equivalent to all ADGs in the equivalence class. Essential graphs are characterized, a polynomialtime algorithm for their construction is given, and their applications to model selection and other statistical
Learning Bayesian Networks by Genetic Algorithms. A case study in the prediction of survival in malignant skin melanoma
, 1997
"... In this work we introduce a methodology based on Genetic Algorithms for the automatic induction of Bayesian Networks from a file containing cases and variables related to the problem. The methodology is applied to the problem of predicting survival of people after one, three and five years of being ..."
Abstract

Cited by 71 (11 self)
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In this work we introduce a methodology based on Genetic Algorithms for the automatic induction of Bayesian Networks from a file containing cases and variables related to the problem. The methodology is applied to the problem of predicting survival of people after one, three and five years of being diagnosed as having malignant skin melanoma. The accuracy of the obtained model, measured in terms of the percentage of wellclassified subjects, is compared to that obtained by the called NaiveBayes. In both cases, the estimation of the model accuracy is obtained from the 10fold crossvalidation method. 1. Introduction Expert systems, one of the most developed areas in the field of Artificial Intelligence, are computer programs designed to help or replace humans beings in tasks in which the human experience and human knowledge are scarce and unreliable. Although, there are domains in which the tasks can be specifed by logic rules, other domains are characterized by an uncertainty inherent...
Learning Probabilistic Networks
 THE KNOWLEDGE ENGINEERING REVIEW
, 1998
"... A probabilistic network is a graphical model that encodes probabilistic relationships between variables of interest. Such a model records qualitative influences between variables in addition to the numerical parameters of the probability distribution. As such it provides an ideal form for combini ..."
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Cited by 36 (1 self)
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A probabilistic network is a graphical model that encodes probabilistic relationships between variables of interest. Such a model records qualitative influences between variables in addition to the numerical parameters of the probability distribution. As such it provides an ideal form for combining prior knowledge, which might be limited solely to experience of the influences between some of the variables of interest, and data. In this paper, we first show how data can be used to revise initial estimates of the parameters of a model. We then progress to showing how the structure of the model can be revised as data is obtained. Techniques for learning with incomplete data are also covered.
Probabilistic Network Construction Using the Minimum Description Length Principle
, 1994
"... Probabilistic networks can be constructed from a database of cases by selecting a network that has highest quality with respect to this database according to a given measure. A new measure is presented for this purpose based on a minimum description length (MDL) approach. This measure is compared wi ..."
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Cited by 28 (1 self)
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Probabilistic networks can be constructed from a database of cases by selecting a network that has highest quality with respect to this database according to a given measure. A new measure is presented for this purpose based on a minimum description length (MDL) approach. This measure is compared with a commonly used measure based on a Bayesian approach both from a theoretical and an experimental point of view. We show that the two measures have the same properties for infinite large databases. For smaller databases, however, the MDL measure assigns equal quality to networks that represent the same set of independencies while the Bayesian measure does not. Preliminary test results suggest that an algorithm for learning probabilistic networks using the minimum description length approach performs comparably to a learning algorithm using the Bayesian approach. However, the former is slightly faster.
BNT structure learning package: documentation and experiments
 Technical Report FRE CNRS 2645). Laboratoire PSI, Universitè et INSA de Rouen
, 2004
"... Bayesian networks are a formalism for probabilistic reasonning that is more and more used for classification task in datamining. In some situations, the network structure is given by an expert, otherwise, retrieving it from a database is a NPhard problem, notably because of the search space comple ..."
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Cited by 16 (1 self)
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Bayesian networks are a formalism for probabilistic reasonning that is more and more used for classification task in datamining. In some situations, the network structure is given by an expert, otherwise, retrieving it from a database is a NPhard problem, notably because of the search space complexity. In the last decade, lot of methods have been introduced to learn the network structure automatically, by simplifying the search space (augmented naive bayes, K2) or by using an heuristic in this search space (greedy search). Most of these methods deal with completely observed data, but some others can deal with incomplete data (SEM, MWSTEM). The Bayes Net Toolbox introduced by [Murphy, 2001a] for Matlab allows us using Bayesian Networks or learning them. But this toolbox is not ’state of the art ’ if we want to perform a Structural Learning, that’s why we propose this package.
The Posterior Probability of Bayes Nets with Strong Dependences
 Soft Computing
, 1999
"... Stochastic independence is an idealized relationship located at one end of a continuum of values measuring degrees of dependence. Modeling real world systems, we are often not interested in the distinction between exact independence and any degree of dependence, but between weak ignorable and strong ..."
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Cited by 14 (1 self)
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Stochastic independence is an idealized relationship located at one end of a continuum of values measuring degrees of dependence. Modeling real world systems, we are often not interested in the distinction between exact independence and any degree of dependence, but between weak ignorable and strong substantial dependence. Good models map significant deviance from independence and neglect approximate independence or dependence weaker than a noise threshold. This intuition is applied to learning the structure of Bayes nets from data. We determine the conditional posterior probabilities of structures given that the degree of dependence at each of their nodes exceeds a critical noise level. Deviance from independence is measured by mutual information. Arc probabilities are determined by the amount of mutual information the neighbors contribute to a node, is greater than a critical minimum deviance from independence. A Ø 2 approximation for the probability density function of mutual info...
Predicting the Survival in Malignant Skin Melanoma Using Bayesian Networks Automatically Induced by Genetic Algorithms  An Empirical Comparision Between Different Approaches
 Artificial Intelligence in Medicine
, 1998
"... In this work we introduce a methodology based on Genetic Algorithms for the automatic induction of Bayesian Networks from a file containing cases and variables related to the problem. The structure is learned by applying three different methods: The Cooper and Herskovits metric for a general Bayesia ..."
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Cited by 13 (5 self)
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In this work we introduce a methodology based on Genetic Algorithms for the automatic induction of Bayesian Networks from a file containing cases and variables related to the problem. The structure is learned by applying three different methods: The Cooper and Herskovits metric for a general Bayesian Network, the Markov Blanket approach and the relaxed Markov Blanket method. The methodologies are applied to the problem of predicting survival of people after one, three and five years of being diagnosed as having malignant skin melanoma. The accuracy of the obtained models, measured in terms of the percentage of wellclassified subjects, is compared to that obtained by the socalled NaiveBayes. In the four approaches, the estimation of the model accuracy is obtained from the 10fold crossvalidation method. Keywords Bayesian Network, Genetic Algorithm, Structure Learning, Model Search, 10fold Crossvalidation 1. Introduction Expert systems, one of the most developed areas in the fiel...
Random Generation of Dags for Graph Drawing
, 2000
"... The Graph Drawing community uses test suites for comparing layout quality and efficiency. Those suites often claim to collect randomly generated graphs, although in most cases randomness is a loosely defined notion. Wepropose a simple algorithm for generating acyclic digraphs with a given number of ..."
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Cited by 11 (1 self)
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The Graph Drawing community uses test suites for comparing layout quality and efficiency. Those suites often claim to collect randomly generated graphs, although in most cases randomness is a loosely defined notion. Wepropose a simple algorithm for generating acyclic digraphs with a given number of vertices uniformly at random. Applying standard combinatorial techniques, we describe the overall shape and average edge density of an acyclic digraph. The usefulness of our algorithm resides in the possibility of controlling edge density of the generated graphs. We have used our technique to build a large test suite of acyclic digraphs with various edge density and number of vertices ranging from 10 to 1000.
Analysis of the behaviour of genetic algorithms when learning Bayesian network structure from data
, 1997
"... In the last few years Bayesian networks have become a popular way of modelling probabilistic relationships among a set of variables for a given domain. For large domains, though, the construction of Bayesian networks is a hard task and the number of possible structures and the number of parameters f ..."
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Cited by 7 (4 self)
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In the last few years Bayesian networks have become a popular way of modelling probabilistic relationships among a set of variables for a given domain. For large domains, though, the construction of Bayesian networks is a hard task and the number of possible structures and the number of parameters for those structures can be huge. Trying to solve this, some researchers have studied how this construction can be automated. This work analyses the behaviour of genetic algorithms when performing such automation. It is shown that the different ways in which genetic algorithms can tackle the problem influence the results. Key words: Bayesian network; Structure learning; Genetic algorithm 1 Introduction In the last few years Bayesian networks have become a popular way of modelling probabilistic relationships among a set of variables for a given domain. Although sometimes experts can create good Bayesian networks from their own experience, it can be a very hard task for large domains. Therefore...